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Propagating Error a Pendulum

  1. Feb 11, 2009 #1
    1. The problem statement, all variables and given/known data

    The length of a string attached to a pendulum is measured with a precision of (+or-)0.2. The time of the oscillation is measured to a precision of (+or-)0.1. How many periods must you measure so that the contribution of the uncertainty in time is smaller than the uncertainty in length, when calculating g?

    2. Relevant equations


    3. The attempt at a solution

    I dont know where to go from here.
    Delta l and T are the error in those measurements.
  2. jcsd
  3. Feb 11, 2009 #2
    The next thing to do is assume that the error is really small relative to the actual value.
    [tex]\delta l << l[/tex] and [tex]\delta T << T[/tex]. I think you might have an error in your equation for g:
    [tex] g +\delta g= (2 \pi)^2 \frac{l+\delta l }{(T+\delta T)^2}[/tex] where [tex] \delta g[/tex] is the error in g.
    If you are familiar with calculus then this comes out to:
    [tex]\delta g = |\frac{\partial g}{\partial l}| \delta l + |\frac{\partial g}{\partial T}| \delta T[/tex]
    If you don't have the luxury of calculus we might need to know what relations for uncertainty you are given to clue you in
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